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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Since <span class="process-math">\(Q(x)/P(x)=1/x\)</span> has a singularity at <span class="process-math">\(x=0\text{,}\)</span> <span class="process-math">\(x=0\)</span> is a singular point. On the other hand, consider</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\begin{aligned}
&amp;x \frac{Q(x)}{P(x)}=x \frac{\alpha x}{x^2}=\alpha,\\
&amp;x^2 \frac{R(x)}{P(x)}=x^2 \frac{\beta}{x^2}=\beta.
\end{aligned}
\end{equation*}
</div>
<p class="continuation">Since both <span class="process-math">\(x \frac{Q(x)}{P(x)}\)</span> and <span class="process-math">\(x^2 \frac{R(x)}{P(x)}\)</span> are analytic at <span class="process-math">\(x=0\text{,}\)</span> <span class="process-math">\(x=0\)</span> is a regular singular point.</p>
<span class="incontext"><a href="sec5_4.html#p-226" class="internal">in-context</a></span>
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